Achchhe Lal

Stochastic Free Vibration of Laminated Composite Plates in Thermal Environments

This work deals with the stochastic free vibration of laminated composite plates subjected to a thermal loading with general boundary conditions by taking into account the randomness in lamina material properties and thermal expansion coefficients. The system equations have been derived based on higher order shear deformation theory incorporating rotary inertia effects. A C 0 finite element method is used for treating the random eigenvalue problem. A mean centered first-order perturbation technique is adopted to examine the stochastic characteristics of thermal free vibration response. The results have been compared with those available in the literature and independent Monte Carlo simulation.

EFFECT OF UNCERTAIN SYSTEM PROPERTIES ON THERMO-ELASTIC STABILITY OF LAMINATED COMPOSITE PLATES UNDER NONUNIFORM TEMPERATURE DISTRIBUTION

Uncertainties in system properties are inherent in all engineering materials. This paper presents the second-order statistics of thermal buckling response of shear deformable laminated composite plate resting on elastic foundation with random system properties under nonuniform tent-like temperature distribution. The mathematical model based on higher-order shear deformation theory [HSDT] is presented. A C0 finite element method in conjunction with first-order perturbation technique is employed to derive the second-order statistics (mean and the standard deviation) of the thermal buckling temperature under nonuniform tent-like temperature distribution. Numerical results have been compared with available results in literatures and independent Monte Carlo simulation.

Thermomechanical Elastic Post-Buckling of Functionally Graded Materials Plate with Random System Properties

This paper presents the stochastic post-buckling response of elastically supported FGM plate with random system properties subjected to uniform and nonuniform temperature change with temperature-dependent and -independent material properties. The FGMs plate is supported with two parameters of Pasternak foundation with Winkler cubic nonlinearity. The basic formulation is based on higher-order shear deformation theory (HSDT) with von-Karman nonlinearity using modified C0 continuity. A direct iterative-based nonlinear finite element method combined with first-order perturbation technique is used to compute the second-order statistics (mean and coefficient of variation) of post-buckling response of FGM plates.

Hygrothermoelastic free vibration response of laminated composite plates resting on elastic foundations with random system properties Micromechanical model

This article presents the hygrothermal effects on the free vibration of laminated composite plates resting on a two-parameter Winkler and Pasternak elastic foundations with random system properties using micromechanical model. System properties such as material properties, hygroscopic expansion coefficients, thermal expansion coefficients and foundation stiffness parameters are modeled as independent basic random variables which are affected by the variation in temperature and moisture based on a micromechanical model of a laminate for accurate prediction of system behavior. A C 0 finite element method based on higher-order shear deformation theory has been used for deriving the standard eigenvalue problem. A Taylor series-based mean-centered first-order perturbation technique is used to find mean and standard deviation of the natural frequency subjected to uniform moisture concentration and temperature rise, plate aspect ratio, total number of plies, fiber orientations and elastic foundation parameters with different boundary support under hygrothermal environmental conditions. Typical numerical results have been validated with those available in the literature and independent Monte Carlo simulation.

Hygrothermally induced buckling analysis of elastically supported laminated composite plates with random system properties

The article presents hygrothermally induced buckling of geometrically linear laminated composite plates resting on two parameters Pasternak elastic foundation subjected to moisture and temperature-independent and -dependent material properties with random system properties. System properties such as elastic moduli, shear moduli of the constituent materials, hygroscopic contraction coefficients, thermal expansion coefficients, and foundation stiffness parameters are modeled as independent basic random variables. A computationally efficient Cu20090 finite element method combined with Taylor series based mean-centered first-order perturbation technique via higher order shear deformation plate theory is used to solve the random eigenvalue problem. Typical numerical results for dimensional mean and coefficient of variance of hygrothermally induced buckling load of laminated composite plate subjected to uniform hygrothermal loadings are examined with uniform moisture concentration and temperature rise, plate thickness and aspect ratios, total number of plies, fiber orientations, elastic foundations, and different boundary conditions with random system properties. The numerical results obtained by the present solution approach are validated with those available in the literatures and independent Monte Carlo simulation.

Bending analysis of laminated SWCNT Reinforced functionally graded plate Using FEM

Abstract In this paper presents bending characteristic of multi-layered carbon nanotube reinforced functionally graded composite plates. The finite element implementation of bending analysis of laminated composite plate via well-established higher order shear deformation theory(HSDT). A seven degree of freedom and C0 continuity finite element model using nine noded isoperimetric elements is developed for precise computation of ply-by-ply deflection and stresses of laminated Single Wall Carbon Nanotube Reinforced composite plate subjected to uniform transverse loading. The finite element implementation is carried out through a finite element code developed in MATLAB.The results obtained by present approach are compared with results available in the literatures. The effective material properties of the laminated SWCNTRC plate are used by Mori-Tanaka method.Numerical results have been obtained with different parameters, width-to-thickness ratio(a/h), stress distribution profile along thickness direction,different SWCNTRC-FG plate, boundary condition and various lamination schemes.

Stochastic Critical Stress Intensity Factor Response of Single Edge Notched Laminated Composite Plate

Fiber reinforced composite materials are increasingly being used in aircraft and automotive industries due to their outstanding mechanical properties of very high specific strength and stiffness, better corrosion and fatigue resistance and tailoring ability. During manufacturing and processing, these material structures are subjected to discontinuities in the form of holes, notches, and/or cracks. The presences of these discontinuities in the structures influence the stress distribution, and the stresses around a crack tip increase extraordinarily. In such a condition, it is necessary to consider fracture mechanics parameters known as critical stress intensity factor or toughness of the materials against crack growth under external loadings. To accurately predict the fracture response in terms of stress

Uncertainty quantification in non-linear dynamic response of functionally graded materials plate

ABSTRACT This study deals with the stochastic non-linear dynamic response of functionally graded materials (FGMs) plate with uncertain system properties subjected to time-dependent uniformly distributed transverse load in thermal environments. System properties, such as material properties of each constituents material, volume fraction index, and transverse load, are taken as uncorrelated random input variables. Material properties are assumed as temperature dependent (TD). The formulation is based on higher-order shear deformation theory (HSDT) with von-Karman non-linear strain kinematics using modified C° continuity. A Newton–Raphson-based non-linear finite element method along with a first-order perturbation technique (FOPT) and Monte Carlo sampling (MCS) is outlined to examine the second-order statistics (mean, standard deviation (SD), and probability density function (PDF)) of the non-linear dynamic response of the FGM plate. The governing dynamic equation is solved by Newmarks time integration scheme. The effects of volume fraction index, load parameters, plate thickness ratios, and temperature changes with random system properties are examined through parametric studies. The present outlined approach is validated with the results available in the literature and by MCS.

Stochastic Thermal Free Vibration Response of Laminated Composite Plates Resting on Elastic Foundation with Uncertain Material Properties

This study deals with the stochastic free vibration response of a laminated composite plate resting on a elastic foundation subjected to a temperature loading with uncertain material properties. The material properties are modeled as independent basic random variables. The temperature field considered is assumed to be a uniform distribution over the plate surface and through the plate thickness. The material properties are assumed to be independent of temperature. Based on the higher order deformation theory, C0 finite element method is employed to derive the eigen value problems in term of fundamental frequency. A mean-centered first order perturbation technique (FOPT) is adopted to evaluate the mean and standard derivation of the fundamental frequency with all edges simply supported boundary conditions. The effects of foundation parameters on the critical temperature are analyzed. The results have been validated with independent Monte Carlo simulation (MCS) and those available in the literature.

Stochastic critical stress intensity factor response of single edge notched laminated composite plate using displacement correlation method

Abstract The second-order statistics of critical stress intensity factor (SIF) of single edge notched fiber reinforced composite plates with random system properties and subjected to uniaxial tensile loadings is investigated. This paper is an extension of reference (Lal and Kapania, 2013) by the present authors by considering more number of input random system parameters for higher accuracy. A C0 finite element method based on a higher-order shear deformation plate theory using displacement correlation method via isoparametric quarter point element is proposed for basic formulation. A stochastic finite element method using first-order perturbation technique and Monte Carlo simulation (MCS) is employed to examine the mean, coefficient of variance, and probability density faction of critical first mode SIF. The effect of different fiber orientations, crack length, plate thickness, a number of layers, and the lamination schemes with random system properties on the statistics of SIF of single edge crack laminated composite plate is evaluated. The tensile failure load is predicted using Hashin’s failure criteria. The present approach is validated with results available in literature and by employing independent MCS.